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1. Simulation of ductile failure of a notched-tension specimen of 3D printed 316L stainless steel

   https://doi.org/10.1007/s10704-025-00851-5  

   Xie, Jianing; Ravi-Chandar, Krishnaswamy (August 2025, International Journal of Fracture)

   The rapid development of 3D printing of 316L stainless steel thin-walled structures obtained by direct energy deposition has generated an increased interest in the mechanical properties of such materials for use in applications; in particular, failure models are needed to ensure structural reliability. We consider the response of uniaxial tenson specimens, with and without notches, to characterize the constitutive and failure behavior of the material. Specifically, we use numerical simulations of the notched tension experiment, achieved with a simple power- law strain hardening model and a failure criterion based on attaining a triaxiality-dependent critical strain-to-failure, to demonstrate that this model is capable of reproducing the material behavior accurately. 

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2. Artificial neural network enhanced plasticity modelling and ductile fracture characterization of grade-1 commercial pure titanium

   https://doi.org/10.1016/j.ijplas.2024.104044  

   Ebrahim, Abrar Salam; Zhang, Qi; Ha, Jinjin (June 2024, International Journal of Plasticity)

   This study primarily aims to develop a robust modelling approach to capture complex material behavior of CP-Ti, appeared by high anisotropy, differential hardening due to anisotropy evolution, and flow behavior sensitive to strain rate and temperature, using artificial neural networks (ANNs). Plasticity is characterized by uniaxial tension and in-plane biaxial tension tests at temperatures of 0°C and 20°C with strain rates of 0.001 /s and 0.01 /s, and the results are used to calibrate the non-quadratic anisotropic Yld2000-3d yield function with respect to the plastic work. In order to predict the intricate plastic deformation with the temperature and strain rate effects, two distinct ANN models are developed; one is to capture the strain hardening behavior and the other to predict the anisotropic parameters in the chosen yield function. The developed ANN models predict an unseen dataset well, which is intermediate testing conditions at a temperature of 10°C and strain rate of 0.005 /s. The ANN models, being computationally stable and adhering to conventional constitutive equations, are implemented into a user material subroutine for the ductile fracture characterization of CP-Ti sheet using the hybrid experimental-numerical analysis. The favorable agreement between experimental data and numerical predictions, particularly using the ANN models with evolving anisotropic material parameters for the Yld2000-3d yield function, underscores the significance of differential hardening effect on the ductile fracture behavior and highlights the capabilities of ANN models to capture the complex plastic behavior of CP-Ti. The key parameters including stress triaxiality, Lode angle parameter, and equivalent plastic strain at the fracture location are extracted from the simulations, enabling the calibration of ductile fracture models, namely Johnson-Cook, Hosford-Coulomb, and Lou-2014, and construction of fracture envelopes. 

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3. On the Transversely Isotropic, Hyperelastic Response of Central Nervous System White Matter Using a Hybrid Approach

   https://doi.org/10.1115/1.4049168  

   Pan, Yi; Shreiber, David I.; Pelegri, Assimina A. (February 2021, Journal of Engineering and Science in Medical Diagnostics and Therapy)

   Abstract A numerical and experimental hybrid approach is developed to study the constitutive behavior of the central nervous system white matter. A published transversely isotropic hyperelastic strain energy function is reviewed and used to determine stress–strain relationships for three idealized, simple loading scenarios. The proposed constitutive model is simplified to a three-parameter hyperelastic model by assuming the white matter's incompressibility. Due to a lack of experimental data in all three loading scenarios, a finite element model that accounts for microstructural axons and their kinematics is developed to simulate behaviors in simple shear loading scenarios to supplement existing uniaxial tensile test data. The parameters of the transversely isotropic hyperelastic material model are determined regressively using the hybrid data. The results highlight that a hybrid numerical virtual test coupled with experimental data, can determine the transversely isotropic hyperelastic model. It is noted that the model is not limited to small strains and can be applied to large deformations. 

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4. Identification of Yld2000–2d anisotropic yield function parameters from single hole expansion test using machine learning

   https://doi.org/10.1016/j.cirp.2024.04.026  

   Kim, Jinjae; Ebrahim, Abrar S; Kinsey, Brad L; Ha, Jinjin (May 2024, CIRP Annals)

   This study presents a novel machine learning approach for predicting the anisotropic parameters of the Yld20002d non-quadratic yield function using a hole expansion test. Heterogeneous stress-strain fields during the test substitute for multiple experiments required in the conventional parameter identification approach. An artificial neural network model for the parameter prediction is developed using a virtually generated training dataset composed of strains from hole expansion simulations, performed using randomly selected anisotropic parameters. The developed model predicts the Yld20002d parameters for AA6022-T4 based on the measured strain field from a hole expansion experiment, and the parameter results are evaluated by comparing anisotropy in uniaxial tension tests, the yield locus, and thinning variation in hole expansion test. 

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5. A new constitutive relation to describe the response of bones

   https://doi.org/10.1016/j.ijnonlinmec.2024.104664  

   Arumugam, J; Alagappan, P; Bird, J; Moreno, M; Rajagopal, KR (May 2024, International Journal of Non-Linear Mechanics)

   Trabecular bone, a solid that has a heterogeneous porous structure, demonstrates nonlinear stress–strain relationship, even within the small strain region, when subject to stresses. It also exhibits different responses when subject to tension and compression. This study presents the development of an implicit constitutive relation between the stress and the linearized strain specifically tailored for trabecular bone-like materials. The structure of the constitutive relation requires the solution of the balance of linear momentum and the constitutive relations simultaneously, and in view of this, a two-field mixed finite element model capable of solving general boundary value problems governed by a system of coupled equations is proposed. We investigate the effects of nonlinearity and heterogeneity in a dogbone-shaped sample. Our study is able to capture the significant nonlinear characteristics of the response of the trabecular bone undergoing small strains in experiments, in both tension and compression, very well. 

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